Exponential Graphs

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase as time progresses.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease as time progresses.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph will show a curve that either rises steeply (growth) or falls steeply (decay) and will not form a straight line.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the x-axis but never touches it.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function falls steeply to the right and approaches the x-axis but never touches it.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is the x-axis (y=0), which the graph approaches but never reaches.

Front

What happens to f(x) as x approaches infinity in an exponential growth function?

Back

As x approaches infinity in an exponential growth function, f(x) approaches infinity.

Front

What happens to f(x) as x approaches negative infinity in an exponential decay function?

Back

As x approaches negative infinity in an exponential decay function, f(x) approaches the value of a (the y-intercept).

Front

What is the y-intercept of the function f(x) = 2(1/7)^x?

Back

The y-intercept of the function f(x) = 2(1/7)^x is 2, which occurs when x=0.